CN111640080B - CS image denoising reconstruction method based on hyperspectral total variation - Google Patents
CS image denoising reconstruction method based on hyperspectral total variation Download PDFInfo
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Abstract
The invention provides a CS image denoising reconstruction method based on hyperspectral total variation, which comprises the following steps: initializing a reconstructed image, an iteration index value and a noisy observation value; iteratively updating the obtained reconstructed image by using the noisy observation value to obtain an estimated value; the estimated values are respectively input to the basel 1-obtaining an intermediate reconstructed image in a CS reconstruction model of the norm and HTV; sparse representation is carried out on the intermediate reconstructed image by using Starlet transformation to obtain a Starlet coefficient; carrying out drying filtering on the Starlet coefficient by using a new threshold operator and an improved BayEslim threshold to obtain a curvelet coefficient; performing Starlet inverse transformation on the curvelet coefficient to obtain a reconstructed image; and judging whether the iteration stopping condition is met or not, and circulating iteration. The invention can effectively protect the characteristic information such as details, textures and the like in the image while removing most of noise information in the high-noise image, has simple realization and stronger robustness, and effectively solves the problem of denoising reconstruction of the high-noise image.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to a CS image denoising reconstruction method based on hyperspectral total variation, which is used for denoising reconstruction of high-noise images and realizes high-efficiency denoising capability of high-resolution images under a high-noise condition.
Background
With the continuous progress of modern science and technology, the CMOS/CCD sensor technology has also been developed rapidly, and the impact on us is mainly reflected in two aspects: (1) the image quality is higher and higher; (2) image resolution is becoming higher and higher. High resolution images, while providing us with extremely high visual enjoyment, also present new challenges to the image processing field. When high-resolution image capturing is performed at night, image data obtained in general contains a large amount of noise information due to the influence of the night environment; in addition, when shooting is performed in a complicated and noisy environment, a high-noise and high-resolution image inevitably appears. High resolution images containing high noise information have important effects on extracting important feature information in images, performing effective data analysis and visual quality, and it is difficult to maximally mine effective information in images from high noise images. In some cases, it is not even possible to directly process high resolution, high noise images. Therefore, the denoising problem of high-resolution images under high-noise conditions is an important scientific problem faced by scholars at home and abroad at present. Aiming at denoising a high-noise high-resolution image, how to design a high-efficiency and high-quality reconstruction method is a hot spot of research in every country scientist.
In order to effectively solve the problem of reconstruction of high-dimensional signals/images, Donoho et al propose a well-known Compressed Sensing (CS) theory. The theory breaks the limitations of the nyquist sampling theorem and can realize high-quality reconstruction of high-resolution signals/images by using only a small amount of observation data. The CS theory has been developed over 10 years and has been successfully applied to various fields. The CS theory mainly consists of three parts: sparse transformation process, measurement matrix design and reconstruction algorithm design process. If the signal has sparsity on a certain sparse basis (sparse transform), the signal can be projected on the sparse basis to obtain a sparse coefficient, then the obtained sparse coefficient is screened by using a measurement matrix, a small amount of measured value information is extracted, and finally the designed reconstruction algorithm is used for reconstructing the original signal with high quality by using only a small amount of measured values. It can be seen that the reconstruction process of CS is also a de-noising reconstruction process in nature. The invention focuses on the design of sparse transformation or the design of a selection process and a reconstruction algorithm, and a random measurement matrix is adopted as a measurement matrix.
The existing sparse transform usually adopts a wavelet transform process, and in the process of image sparse representation, the wavelet transform is difficult to effectively separate image data information from noise information to the maximum extent, so that the reconstruction effect of an image is influenced. The CS reconstruction algorithm is the most important step in the CS implementation process, and directly determines the reconstruction quality and the reconstruction accuracy of the image. However, the currently designed CS reconstruction algorithms are capable of achieving high quality reconstructions for low noise or noise-free images. However, for the reconstruction process of the high-noise image, how to add an effective filtering process of the image data in the image reconstruction process is not fully considered, and then the denoising reconstruction effect of the image is also influenced.
Therefore, a high-performance sparse transformation method must be selected or designed, so that the image data and the noise information can be effectively separated to the maximum extent; meanwhile, the CS denoising reconstruction method with high reconstruction accuracy is designed to effectively solve the denoising reconstruction problem of the high-resolution image under the high-noise condition.
Disclosure of Invention
Aiming at the technical problem that the existing CS reconstruction method is poor in denoising reconstruction performance of a high-noise image, the invention provides a CS image denoising reconstruction method based on hyperspectral total variation.
In order to achieve the purpose, the technical scheme of the invention is realized as follows: a CS image denoising and reconstructing method based on hyperspectral total variation comprises the following steps:
the method comprises the following steps: initializing parameters, iteration index values and noise-containing observation values of a reconstructed image;
step two: iteratively updating the obtained reconstructed image by using the noisy observation value to obtain an updated estimation value;
step three: respectively inputting the estimated values of the second step into the base I1-averaging the reconstruction results obtained in the CS reconstruction model of norm and HTV to obtain an intermediate reconstructed image;
step four: sparse representation is carried out on the intermediate reconstructed image in the third step by using Starlet transformation, and a Starlet coefficient of the intermediate reconstructed image is obtained;
step five: denoising and filtering the Starlet coefficient obtained in the fourth step by using a new threshold operator and an improved BayEslim threshold to obtain a Starlet coefficient of a reconstructed image after denoising;
step six: performing Starlet inverse transformation on the Starlet coefficient of the reconstructed image after noise reduction to obtain a reconstructed image;
step seven: judging whether an iteration stop condition is met: if the condition of stopping iteration is met, stopping the iteration process and outputting the obtained reconstructed image; otherwise, adding 1 to the iteration index value, and circularly repeating the step two to the step six.
The reconstructed image x initialized in the first step 00 and x1＝ΦTy, the iteration index s is 0, and the observed value y containing noise is phi x + epsilon phi psi eta + epsilon; wherein phi is a random measurement matrix, x is an input original clear image with the size of NxN, epsilon represents white Gaussian noise, and psi is a Starlet transformation matrix; eta ═ ΨTx is a sparse coefficient obtained by Starlet transformation of an original clear image;
the method for obtaining the updated estimation value by carrying out iterative update in the second step comprises the following steps:
xs+1＝xs+ΦT(y-Φxs) (1)
wherein x issAnd xs+1Representing the estimated values of the reconstructed image for the s-th iteration and the s + 1-th iteration, respectively.
Based on l in the third step1The CS reconstruction model of the norm is:
wherein, x'1Is based on l1-reconstructed images obtained by CS reconstruction modeling of the norm, λ being an adjustable parameter,
a penalty term is represented for estimating a deviation between the estimate and the observed value,
representing the prior information of the original image.
The CS reconstruction model based on the HTV in the third step is
Wherein, x'2Is a reconstructed image obtained from an HTV-based CS reconstruction model; beta is an adjustable parameter, and lambda is less than beta, | | xs+1||HTVAn HTV model representing the image for representing original prior total variation data information of the image.
Intermediate reconstructed image x 'obtained by CS reconstructed model in step three's+1Comprises the following steps:
wherein | | | xs+1||HTVThe calculation process of (2) is as follows:
r represents the number of iteration indexes, and R is 10 the maximum
Large number of calculations;
and | | | xs+1||TVThe calculation process of (2) is as follows:
m and N respectively represent the spatial positions of the image pixels, wherein m is more than or equal to 0, and N is more than or equal to N.
And step five, new threshold operator rho (x's+1) Comprises the following steps:
wherein γ is an adjustment parameter, and γ is set as an iteration index s, that is, γ ═ s;
in order to improve the bayesian spring threshold,
in order to be the standard deviation of the noise,
the calculation was done using a robust median method:
χm,nfor the Starlet transform coefficients of the original noisy image after adding noise, Median (| χ)m,n|) denotes all | χm,nI, arranging the data in the middle according to the sequence, and sign () representing a sign function; the standard deviation of an original noisy image of size nxn is
Is the standard deviation of the original sharp image x.
The Starlet coefficient of the reconstructed image after noise reduction is as follows:
α′s+1＝ρ(αs+1) (6)；
starlet coefficient alpha of intermediate reconstructed image in the fourth steps+1Comprises the following steps:
αs+1＝<x′s+1,Ψ> (5)。
wherein Ψ is a Starlet transformation matrix, and < > represents solving an inner product;
in the sixth step, the reconstructed image obtained by using the Starlet inverse transform is as follows:
wherein the content of the first and second substances,
represents the reconstructed image obtained from the (s + 1) th iteration, and T represents the transpose of the matrix. A
The condition that the iteration in the step seven stops is that the difference value of the reconstructed image and the reconstructed image of the last iteration is l2The norm is greater than or equal to a set parameter, namely:
wherein the content of the first and second substances,
and
respectively representing the reconstructed images obtained by the s-th iteration and the s + 1-th iteration,
is a set small value.
The invention has the beneficial effects that: the sparse representation process of the high-noise image is carried out by adopting Starlet transformation, so that the image data and the noise information can be effectively separated, powerful support is provided for the effective screening and image reconstruction of the subsequent image data, and the problem that the noise information and the image data information cannot be effectively analyzed to the maximum extent by wavelet transformation is solved; meanwhile, in order to obtain high-quality image reconstruction, the invention establishes the method based on l1CS reconstruction model of norm and HTV (Hyperspectral Total Variation), which is high-noise imageThe high-quality image provides guarantee; in order to improve the screening capability of the Starlet coefficient of the obtained high-noise image and remove noise information hidden in image data, a new threshold denoising operator is provided, and the data information of the image is screened in an iteration process by improving a Bayesian Shrink threshold. Aiming at the high-noise high-resolution image, the method can effectively protect the characteristic information such as details, textures and the like in the image while removing most of noise information in the high-noise image, can reconstruct the high-quality high-resolution image, and has important significance for the effective analysis and the characteristic extraction of subsequent high-resolution image data and the high-noise image processing in the night environment. The invention has simple realization and stronger robustness, and effectively solves the problem of denoising reconstruction of high-noise images.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 shows the standard deviation of noise in the present invention
In the case of reconstructed images obtained at different Compression Sampling Ratios (CSR), where (a) is an original target paper image, (b) is an original window image, (c) is an original air-conditioned image, (d) is a noise image of (a), (e) is a noise image of (b), (f) is a noise image of (c), (g) is a reconstructed image of (d) when CSR is 0.1, (h) is a reconstructed image of (e) when CSR is 0.1, (i) is a reconstructed image of (f) when CSR is 0.1, (j) is a reconstructed image of (d) when CSR is 0.3, (k) is a reconstructed image of (e) when CSR is 0.3, (l) is a reconstructed image of (f) when CSR is 0.3, (m) is a reconstructed image of (d) when CSR is 0.5, (n) is a reconstructed image of (e) when CSR is 0.5,(o) is the reconstructed image of (f) when the CSR is 0.5.
FIG. 3 is a Peak Signal to Noise Ratio (PSNR) comparison graph of the reconstructed target paper image of the present invention, wherein (a) is the Noise standard deviation
In the case of different compression sampling ratios, a Peak Signal to Noise Ratio (PSNR) comparison result graph obtained by reconstructing a target paper image is obtained, and (b) is a PSNR comparison result graph obtained under different Noise standard deviations when the compression sampling Ratio is 0.3.
FIG. 4 is a graph of the noise standard deviation of the present invention
In the case of local feature images obtained when the CSR varies, the image (a) is an original target paper image, (b) is an original window image part, (c) is an original air-conditioned image part, (d) is a noise image part of (a), (e) is a noise image of (b), (f) is a noise image of (c), (g) is a reconstructed image of (d) when the CSR is 0.1, (h) is a reconstructed image of (e) when the CSR is 0.1, (i) is a reconstructed image of (f) when the CSR is 0.1, (j) is a reconstructed image of (d) when the CSR is 0.3, (k) is a reconstructed image of (e) when the CSR is 0.3, (l) is a reconstructed image of (f) when the CSR is 0.3, (m) is a reconstructed image of (d) when the CSR is 0.5, (n) is a reconstructed image of (e) when the CSR is 0.5, and (o) is a reconstructed image of (f) when the CSR is 0.5.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
The idea of the invention is that: (1) use design base of l1Iteratively updating the obtained reconstructed image by the CS reconstruction model of the norm and the HTV; (2) in the CS sparse transform processThe image data and the noise data can be effectively separated to the maximum extent by adopting Starlet transformation; (3) by adopting the designed new threshold operator, the obtained Starlet coefficient is effectively screened by using the improved Bayesian Shrink threshold in each iteration process, so that more image detail characteristic information can be reserved, and the reconstruction quality of a high-resolution image is improved.
The hardware environment for implementing the invention is as follows: intel (R) core (TM) i5 CPU 2.5G computer, 8G memory, running software environment: MATLAB2014b, operating system Windows 7. The image data was obtained by using an SP-20000M-PMCL black-and-white industrial camera of SPARK series manufactured by JAI.
As shown in fig. 1, a CS image denoising and reconstructing method based on hyperspectral total variation includes the following steps:
the method comprises the following steps: and initializing parameters, iteration index values and noise-containing observation values of the reconstructed image.
Initializing a reconstructed image x00 and x1＝ΦTy, an iteration index s is 0, and a noise-containing observation value y is phi x + epsilon and phi psi eta + epsilon; wherein phi is a random measurement matrix, x is an input original clear image with the size of NxN, epsilon represents white Gaussian noise, and psi is a Starlet transformation matrix; eta ═ ΨTx is the sparse coefficient obtained by the Starlet transform.
Step two: and carrying out iterative updating on the obtained reconstructed image to obtain an updated estimation value.
For the obtained reconstructed image x00 and x1＝ΦTy are iteratively updated to obtain an updated estimated value xs+1：
xs+1＝xs+ΦT(y-Φxs) (1)
Wherein x issAnd xs+1Representing the estimated values of the reconstructed image for the s-th iteration and the s + 1-th iteration, respectively.
Step three: respectively inputting the estimated values obtained in the step two into the base I1-averaging the reconstruction results obtained in the CS reconstruction model of norm and HTV to obtain an intermediate reconstructed image.
Obtaining a reconstructed image x 'according to the CS reconstruction model's+1：
Wherein the content of the first and second substances,
wherein, x'1Is according to l1-reconstructed image x 'obtained by norm reconstruction model'2A reconstructed image obtained from the HTV reconstruction model; λ and β are both different adjustable parameters, and λ < β is required to suppress the occurrence of a step effect in the reconstructed image, where λ is 0.2 and β is 0.32.
At the same time, | xs+1||HTVThe calculation process of (2) is as follows:
r represents the iteration index number, and R is 10, which is the maximum number of computations. And | | | xs+1||TVThe calculation process of (2) is as follows:
Step four: and (4) performing sparse representation on the intermediate reconstructed image obtained in the step three by using Starlet transformation to obtain a Starlet coefficient of the intermediate reconstructed image.
Reconstructed image x 'obtained by Starlet transform pair's+1Performing multi-scale decomposition, and obtaining Starlet coefficient alpha of reconstructed image when performing multi-scale Starlet decompositions+1Comprises the following steps:
αs+1＝<x′s+1,Ψ> (5)。
step five: and denoising and filtering the obtained Starlet coefficient by using a newly-proposed threshold operator and an improved BayEslim threshold to obtain the Starlet coefficient of the reconstructed image after denoising, and effectively removing noise information hidden in the reconstructed image.
The newly proposed threshold operator ρ (x's+1) Comprises the following steps:
where γ is an adjustment parameter, and is set as an iteration index s, that is, γ ═ s;
in order to improve the bayesian spring threshold,
for noise standard deviation, a robust median method can be used for calculation:
χm,nfor the Starlet transform coefficients of the original noisy image after adding noise, Median (| χ)m,n|) denotes all | χm,nThe data in the middle is taken out in order. sign () represents a sign function. For an N × N original noisy image, its standard deviation calculation process is
Standard deviation of original sharp image x
Denoising the Starlet coefficient of the reconstructed image obtained in the step four by using a new threshold operator rho (x), and obtaining the Starlet coefficient of the reconstructed image after denoising:
α′s+1＝ρ(αs+1) (6)。
step six: and performing Starlet inverse transformation on the Starlet coefficient of the reconstructed image after noise reduction to obtain the reconstructed image.
Reconstructed images were obtained using Starlet inverse transformation:
wherein the content of the first and second substances,
representing the reconstructed image from the (s + 1) th iteration and T representing the transpose of the matrix.
Step seven: judging whether an iteration stop condition is met: if the condition of iteration stop is satisfied, i.e. the difference value of the reconstructed image and the reconstructed image of the last iteration is l2Stopping the iteration process when the norm is greater than or equal to the set parameter, and outputting the obtained reconstructed image; otherwise, if the condition of stopping iteration is not met, the iteration index s is made to be s +1, and the steps two to six are continuously repeated.
Judging whether the iteration stop condition is met:
wherein the content of the first and second substances,
is a set small value. Outputting the obtained reconstructed image if the iteration stop condition is satisfied
And if the iteration stopping condition is not met, making the iteration index s equal to s +1, simultaneously returning to the step two, and repeating the processes from the step two to the step six.
The implementation steps of the invention are as follows: initializing a reconstructed image parameter, an iteration number parameter and a noisy observed value; use design base of l1CS reconstruction model pair of norm and HTVIteratively updating the obtained reconstructed image; performing sparse representation on the obtained reconstructed image by using a Starlet conversion process, and effectively separating image data from noise information; effectively screening the obtained Starlet coefficient by using an improved Bayesian Shrink threshold value through a designed new threshold operator, and removing noise information hidden in image data; carrying out an inverse transformation process on the screened Starlet coefficient to obtain a reconstructed image; and judging whether an iteration stopping condition is reached, outputting the obtained reconstructed image when the iteration stopping condition is reached, and otherwise, repeating the process.
The effectiveness of the invention is evaluated by subjective and considerable evaluation methods. The subjective evaluation method directly evaluates the quality of a reconstructed image mainly by a human visual system, as shown in fig. 2 and 4. Fig. 2 (a) - (c) show images of original target paper, window and air conditioner photographed in 2048 × 2048 size; FIGS. 2 (d) - (f) show the addition of noise standard deviations to the three original images
Obtaining a noise-containing target paper, a noise-containing window and a noise-containing air conditioner image by using the noise; fig. 2 (g) - (i) show the reconstruction results obtained by the present invention for the noisy target paper, noisy window and noisy air-conditioning image, respectively, when the CSR is 0.1; the CSR is defined as the ratio of the dimension of the obtained reconstruction observation value to the dimension of the original image, and the smaller the value of the CSR is, the less measurement data is needed for reconstructing the image; the more vice versa. Comparing (d) - (f) in fig. 2 and (g) - (i) in fig. 2, respectively, it can be seen that, in the case of low CSR, the present invention can remove most of the noise information in the image and reconstruct a high-quality image. Fig. 2 (j) - (l) show the reconstruction results obtained by the present invention for the noisy target paper, noisy window and noisy air-conditioning image, respectively, when the CSR is 0.3; fig. 2 (m) - (o) show the reconstruction results obtained by the present invention for the noisy target paper, noisy window and noisy air-conditioning image, respectively, at a CSR of 0.5; as can be seen from (g) - (o) in fig. 2, as the CSR increases, the PSNR value obtained by the present invention also gradually increases, and the quality of the obtained reconstructed image also improves. FIG. 4 shows the invention at a noise standard deviation ofAnd at 30, reconstructing the obtained local characteristic image. Fig. 4 (a) - (c) show local target paper features, local window features and local air conditioning feature images of size 1024 × 1024 taken from original target paper, window and air conditioning images of size 2048 × 2048 taken respectively; FIGS. 4 (d) - (f) show the local feature image plus noise standard deviation
Respectively obtaining a noise-containing local target paper characteristic, a noise-containing local window characteristic and a noise-containing local air conditioner characteristic image; fig. 4 (g) - (i) show the reconstruction results obtained by the present invention for the images of the noisy local target paper feature, the noisy local window feature and the noisy local air-conditioning feature, respectively, when the CSR is 0.1; fig. 4(j) - (l) show the reconstruction results obtained for the images of the noisy local target paper feature, the noisy window local feature and the noisy air-conditioning local feature, respectively, according to the present invention when the CSR is 0.3; fig. 4 (m) - (o) show the reconstruction results obtained for the images of the noisy local target paper feature, the noisy window local feature and the noisy air-conditioning local feature, respectively, when the CSR is 0.5; as can be seen from FIGS. 4(j) - (o), the present invention can preserve more detail features of the image and reconstruct a high quality image.
The objective evaluation method is mainly used for finishing the evaluation of the quality of the reconstructed image by using a specific formula through an established mathematical model. Fig. 3 (a) shows PSNR obtained by reconstructing an image of a noisy target paper under different CSR conditions according to the present invention when the noise standard deviation is 30; it can be seen that the PSNR obtained by the present invention gradually increases with the increase of CSR, and the present invention can also obtain a higher PSNR value at low CSR. Fig. 3 (b) shows PSNR obtained by reconstructing the noisy target paper image under different noise standard deviations according to the present invention when the compression sampling ratio is 0.3; it can be seen that as the standard deviation of the noise increases, the noise information gradually increases, and the invention can obtain a higher PSNR value for the denoising reconstruction of the high-noise image. Meanwhile, with the increase of noise information, the PSNR value of the invention has slower reduction rate and shows stronger robustness.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (10)
1. A CS image denoising and reconstructing method based on hyperspectral total variation is characterized by comprising the following steps:
the method comprises the following steps: initializing parameters, iteration index values and noise-containing observation values of a reconstructed image;
step two: iteratively updating the obtained reconstructed image by using the noisy observation value to obtain an updated estimation value;
step three: respectively inputting the estimated values of the second step into the base I1-averaging the reconstruction results obtained in the CS reconstruction model of norm and HTV to obtain an intermediate reconstructed image;
step four: sparse representation is carried out on the intermediate reconstructed image in the third step by using Starlet transformation, and a Starlet coefficient of the intermediate reconstructed image is obtained;
step five: denoising and filtering the Starlet coefficient obtained in the fourth step by using a new threshold operator and an improved BayEslim threshold to obtain a Starlet coefficient of a reconstructed image after denoising;
step six: performing Starlet inverse transformation on the Starlet coefficient of the reconstructed image after noise reduction to obtain a reconstructed image;
step seven: judging whether an iteration stop condition is met: if the condition of stopping iteration is met, stopping the iteration process and outputting the obtained reconstructed image; otherwise, adding 1 to the iteration index value, and circularly repeating the step two to the step six.
2. The denoising reconstruction method for CS image based on hyperspectral total variation as claimed in claim 1, wherein the reconstructed image x initialized in the first step is00 and x1＝ΦTy, the iteration index s is 0, and the observed value y containing noise is phi x + epsilon phi psi eta + epsilon; where Φ is a random measurement matrix, x is the input raw clear image of size NxN, ε represents white Gaussian noise, Ψ is Stan arlet transformation matrix; eta ═ ΨTx is a Starlet coefficient obtained by the Starlet transformation of the original clear image;
the method for obtaining the updated estimation value by carrying out iterative update in the second step comprises the following steps:
xs+1＝xs+ΦT(y-Φxs) (1)
wherein x issAnd xs+1Representing the estimated values of the reconstructed image for the s-th iteration and the s + 1-th iteration, respectively.
3. The CS image denoising and reconstructing method based on hyperspectral total variation as claimed in claim 2, wherein l is based in the third step1The CS reconstruction model of the norm is:
wherein, x'1Is based on l1-reconstructed images obtained by CS reconstruction modeling of the norm, λ being an adjustable parameter,
a penalty term is represented for estimating a deviation between the estimate and the observed value,
representing the prior information of the original image.
4. The CS image denoising and reconstructing method based on hyperspectral total variation as claimed in claim 3, wherein the HTV-based CS reconstruction model in the third step is
Wherein, x'2For reconstruction maps obtained from HTV-based CS reconstruction modelsAn image; beta is an adjustable parameter, and lambda is less than beta, | | xs+1||HTVAn HTV model representing the image for representing original prior total variation data information of the image.
5. The CS image denoising and reconstructing method based on hyperspectral total variation as claimed in claim 4, wherein the intermediate reconstructed image x 'obtained by the CS reconstruction model in step three's+1Comprises the following steps:
6. the denoising reconstruction method for the CS image based on the hyperspectral total variation according to claim 4, wherein | | ×s+1||HTVThe calculation process of (2) is as follows:
r represents the iteration index number, and R is 10 which is the maximum calculation number;
and | | | xs+1||TVThe calculation process of (2) is as follows:
m and N respectively represent the spatial positions of the image pixels, wherein m is more than or equal to 0, and N is more than or equal to N.
7. The denoising reconstruction method for the CS image based on the hyperspectral total variation according to claim 1, 5 or 6, wherein the new threshold operator p (x) in the fifth steps′+1) Comprises the following steps:
wherein gamma is an adjusting parameter, gamma is set as an iteration index s,i.e., γ ═ s;
in order to improve the bayesian spring threshold,
in order to be the standard deviation of the noise,
the calculation was done using a robust median method:
χm,nfor the Starlet transform coefficients of the original noisy image after adding noise, Median (| χ)m,n|) denotes all | χm,nI, arranging the data in the middle according to the sequence, and sign () representing a sign function; the standard deviation of an original noisy image of size nxn is
Is the standard deviation of the original sharp image x.
8. The CS image denoising and reconstructing method based on hyperspectral total variation according to claim 7, wherein the Starlet coefficient of the reconstructed image after denoising is:
α′s+1＝ρ(αs+1) (6)；
wherein alpha iss+1The Starlet coefficients for the intermediate reconstructed image.
9. The CS image denoising and reconstructing method based on hyperspectral total variation as claimed in claim 8, wherein the Starlet coefficient α of the reconstructed image in the middle of the step four is alphas+1Comprises the following steps:
αs+1＝<x′s+1,Ψ> (5)；
wherein Ψ is a Starlet transformation matrix, and < > represents solving an inner product;
in the sixth step, the reconstructed image obtained by using the Starlet inverse transform is as follows:
wherein the content of the first and second substances,
represents the reconstructed image obtained from the (s + 1) th iteration, and T represents the transpose of the matrix.
10. The denoising reconstruction method for CS images based on hyperspectral total variation according to claim 1 or 9, wherein the condition for stopping iteration in the seventh step is l of difference value between the reconstructed image and the reconstructed image of the last iteration2The norm is greater than or equal to a set parameter, namely:
wherein the content of the first and second substances,
and
respectively representing the reconstructed images obtained by the s-th iteration and the s + 1-th iteration,
is a set small value.
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